# Rational Numbers Class 8 Extra Questions Maths Chapter 1

### Rational Numbers Class 8 Extra Questions Short Answer Type

Question 13.
Calculate the following: Solution:  Question 14.
Represent the following rational numbers on number lines.
(a) (frac { -2 }{ 3 })
(b) (frac { 3 }{ 4 })
(c) (frac { 3 }{ 2 })
Solution: Question 15.
Find 7 rational numbers between (frac { 1 }{ 3 }) and (frac { 1 }{ 2 }).
Solution: Question 16.
Show that: Solution: Question 17.
If x = (frac { 1 }{ 2 }), y = (frac { -2 }{ 3 }) and z = (frac { 1 }{ 4 }), verify that x × (y × z) = (x × y) × z.
Solution:
We have x = (frac { 1 }{ 2 }), y = (frac { -2 }{ 3 }) and z = (frac { 1 }{ 4 })
LHS = x × (y × z) Question 18.
If the cost of 4(frac { 1 }{ 2 }) litres of milk is ₹89(frac { 1 }{ 2 }), find the cost of 1 litre of milk.
Solution: Question 19.
The product of two rational numbers is (frac { 15 }{ 56 }). If one of the numbers is (frac { -5 }{ 48 }), find the other.
Solution:
Product of two rational numbers = (frac { 15 }{ 56 })
One number = (frac { -5 }{ 48 })
Other number = Product ÷ First number Hence, the other number = (frac { -18 }{ 7 })

Question 20.
Let O, P and Z represent the numbers 0, 3 and -5 respectively on the number line. Points Q, R and S are between O and P such that OQ = QR = RS = SP. (NCERT Exemplar)
What are the rational numbers represented by the points Q, R and S. Next choose a point T between Z and 0 so that ZT = TO. Which rational number does T represent?
Solution: As OQ = QR = RS = SP and OQ + QR + RS + SP = OP
therefore Q, R and S divide OP into four equal parts. Question 21.
Let a, b, c be the three rational numbers where a = (frac { 2 }{ 3 }), b = (frac { 4 }{ 5 }) and c = (frac { -5 }{ 6 }) (NCERT Exemplar)
Verify:
(i) a + (b + c) = (a + b) + c (Associative property of addition)
(ii) a × (b × c) – (a × b) × c (Associative property of multiplication)
Solution:  ### Rational Numbers Class 8 Extra Questions Higher Order Thinking Skills (HOTS)

Question 22.
Rajni had a certain amount of money in her purse. She spent ₹ 10(frac { 1 }{ 4 }) in the school canteen, bought a gift worth ₹ 25(frac { 3 }{ 4 }) and gave ₹ 16(frac { 1 }{ 2 }) to her friend. How much she have to begin with?
Solution:
Amount given to school canteen = ₹ 10(frac { 1 }{ 4 })
Amount given to buy gift = ₹ 25(frac { 3 }{ 4 })
Amount given to her friend = ₹ 16(frac { 1 }{ 2 })
To begin with Rajni had Question 23.
One-third of a group of people are men. If the number of women is 200 more than the men, find the total number of people.
Solution:
Number of men in the group = (frac { 1 }{ 3 }) of the group
Number of women = 1 – (frac { 1 }{ 3 }) = (frac { 2 }{ 3 })
Difference between the number of men and women = (frac { 2 }{ 3 }) – (frac { 1 }{ 3 }) = (frac { 1 }{ 3 })
If difference is (frac { 1 }{ 3 }), then total number of people = 1
If difference is 200, then total number of people
= 200 ÷ (frac { 1 }{ 3 })
= 200 × 3 = 600
Hence, the total number of people = 600

Question 24.
Fill in the blanks:
(a) Numbers of rational numbers between two rational numbers is ………. Solution:
(a) Countless
(b) (frac { 6 }{ 11 })
(c) (frac { -3 }{ 2 })
(d) (frac { 3 }{ 5 })
(e) Commutative
(f) associative
(g) equivalent
(h) (frac { 3 }{ 11 })                   